The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 0 1 1 1 X X^2 1 1 1 0 1 1 1 1 1 1 X^2 X^2 1 1 0 X^2 1 1 1 X 1 X 1 1 1 X^2 1 X X^2 1 X 0 X^2 1 X X 0 X 0 0 0 0 0 0 X^2 X X^2+X X^2+X X X X^2+X X^2+X X^2 X^2 0 X X X^2+X X 0 X X 0 X^2+X X X^2 X^2 X^2 X^2+X X^2+X 0 X^2+X X^2+X X X^2 X^2+X X^2+X X^2+X X X^2 X 0 0 X^2+X X^2+X 0 X X X 0 X 0 X^2+X 0 X^2 X^2 0 X X^2+X X^2 X^2 X^2+X X^2 X^2 X^2 X^2 X^2 0 X^2 X X X 0 0 X 0 0 X 0 0 0 X X^2+X X^2+X X X X^2 X X X^2 0 X^2 X^2+X X^2+X X^2+X 0 X X^2+X X^2+X 0 X^2+X X^2+X X^2 X^2 0 0 X^2 X^2 X^2+X 0 X^2+X X^2+X X^2+X X^2 X^2 X^2+X 0 X^2 X^2 X^2+X X X^2 X X^2 X X^2+X X^2 X^2+X X 0 0 X^2+X X X X^2+X X^2+X X 0 0 X X X^2+X X^2+X X X X X^2 X^2+X 0 0 X^2+X X^2 X^2+X 0 0 0 0 X 0 X X X 0 X^2 0 X X^2+X X^2+X X X^2 X^2 0 0 0 X^2 X^2 X^2+X X X^2+X X X 0 X X^2 X^2+X X^2+X X^2+X X X^2+X X^2+X X^2+X X X 0 X^2 X^2 X^2 0 X^2+X X^2 X^2 X^2 X^2 X^2+X X^2 X^2+X X^2 X^2+X X X^2 X^2+X X^2 0 X X^2+X 0 0 X^2 X^2 0 X^2+X 0 X^2+X 0 X^2+X X^2 X X X^2+X X^2+X X X^2+X X^2 0 0 0 0 X X X^2 X^2+X X X^2 X 0 X 0 X X X^2+X X^2+X 0 X^2 X X X^2 0 X^2 X^2+X X^2+X 0 X 0 X^2 X X^2+X X X^2+X X^2 X^2+X X^2 0 0 X X^2 X X^2 X^2 X^2 X 0 0 X X^2+X X^2 X X^2 X^2 X 0 X^2 0 X^2 0 X 0 X^2 X X 0 X^2 X X^2+X X^2 X 0 X^2 0 X^2 X^2+X X X 0 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 generates a code of length 79 over Z2[X]/(X^3) who´s minimum homogenous weight is 70. Homogenous weight enumerator: w(x)=1x^0+111x^70+282x^72+24x^73+362x^74+132x^75+395x^76+252x^77+492x^78+248x^79+426x^80+208x^81+362x^82+116x^83+231x^84+28x^85+151x^86+16x^87+124x^88+72x^90+38x^92+18x^94+6x^96+1x^120 The gray image is a linear code over GF(2) with n=316, k=12 and d=140. This code was found by Heurico 1.16 in 1.79 seconds.